How do you solve these pair of simultaneous equations? 5x+4y= -6 and 2x+6y= 13

Multiply the first equation by 3:.... 15x + 12y = -18
Multiply the second equation by 2: 4x + 12y = 26
Subtract one from the other:
11x = -44
x = -4
Use this value in the first equation: 5(-4) + 4y = -6 --> -20 + 4y = -6 --> 4y = 14 ---> y = 3.5
Check these values in the second equation: 2(-4) + 6(3.5) = -8 + 21 = 13 [check!]

we need to be able to eliminate one of the variables, so first we have to alter our equations:

multiply the first equation by -2 to get

-10x - 8y = 12

now, multiply the second equation by 5 to get

10x + 30y = 65

now, we can add the two equations together to get

0x + 22y = 77

or, y 77/22 = 3.5

Now, we can plug this back into one of the equations, lets pick the first, to get:

5x + 4*3.5 = -6
5x + 14 = -6
5x = -20
x = -4

Now, let's plug both of these into the original first equation to check our work

5 * -4 + 4 * 3.5 = -6
-20 + 14 = -6

This checks so our work is correct.

There are many ways.

Substitution:
find a value for one variable, relative to the other, then substitute that:

From the first equation:
5x + 4y = -6
5x = - 6 - 4y
x = (- 6 - 4y)/5

use the second equation, and "substitute" the value of x:
2x + 6y = 13
2[(- 6 - 4y)/5] + 6y = 13
(-12/5) + (-8/5)y + 6y = 13
-2.4 - 1.6y + 6y = 13
4.4y = 13 + 2.4 = 15.4
and so on.

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Elimination:
Multiply the second equation by -2.5, then add equations together
-2.5(2x + 6y) = -2.5(13)
-5x - 15y = -32.5
+5x + 4y = -6

sum=
-11y = -38.5
y = -38.5/-11
etc.

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Graphic:
turn both equation into slope-intercept format.
Plot them and find the intersection.

y = (-5/4)x + (-6/4)
y = (-2/6)x + (13/6)

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Making both equal:

(the first step was already done in turning them into slope-intercept format)
(since both are equal to y, then the right-sides must be equal)

(-5/4)x + (-6/4) = (-2/6)x + (13/6)
solve for x

5x+4y=-6 eqn1
2x+6y= 13 eqn2
eqn1 multiply by 3,then we get 15x+12y=-18 eqn3
eqn2 multiply by 2 then we get 4x+12y=26 eqn4
then eqn3-eqn4 we get,11x=-44
x=-4.
put x=-4 in eqn2
that is -8+6y=13
6y=13+8=21
y=21/6=7/2